I couldn't quite figure out how to replace the back without possibly damaging the bamboo around it. If that happened then I would have to do some serious repairs and probably paint the whole set. Not the end of the world but still.

And then one night it came to me how to take out the old broken woven insert

It worked. My husband cut out the old woven insert very carefully. I made a pattern, cut the fabric, slid it into place and edged with blue cording I found at Wal-Mart (yep!) on a small roll for $1.00 per chair